Footage of the handshake as the pair met for lunch at the US embassy in Brussels ahead of a NATO summit on Thursday has gone viral.

As cameras rolled, Macron held on tight to Trump's notorious power grip as the two men sat next to each other, the Frenchman's mouth clenched and eyes firmly fixed at the 70-year-old tycoon's squinty stare.

After some five seconds, Trump was the first to open his hand but Macron insisted on being the last to let go.

"It's not the be-all-and-end-all... but a moment of truth," Macron said.

I don't miss a thing, that's how you get respect.

The French leader had another chance later in the day to be his own man, making a beeline for German Chancellor Angela Merkel to embrace her before turning to greet Trump — who smilingly pumped and wrenched Macron's arm as other leaders laughed.

Macron, who became France's youngest president just three weeks ago, said he does not believe in "the diplomacy of public invective but in bilateral dialogue".

He faces his next diplomatic test on Monday, when he will host Russian President Vladimir Putin at the palace of Versailles outside Paris.